Question

Which test?Determine which chi-square test is appropriate in each of the following settings. Explain your reasoning.

a. Does chocolate help heart-attack victims live longer? Researchers in Sweden randomly selected $1169$people who had suffered heart attacks and asked them about their consumption of chocolate in the previous year. Then the researchers followed these people and recorded whether or not they had died within $8$years.

b. Random-digit-dialing telephone surveys used to exclude cell-phone numbers. If the opinions of people who have only cell phones differ from those of people who have landline service, the poll results may not represent the entire adult population. The Pew Research Center interviewed separate random samples of cell-only and landline telephone users who were less than $30$years old and asked them to describe their political party affiliation

Short answer

a. We should use Chi-square test for independence.

b. We should use Chi-square test for homogeneity.

Step-by-step solution

Part (a) Step 1 : Given information

We have to determine which chi-square test is appropriate for given setting.

Part (a) Step 2 : Simplification

Does chocolate help those who have had a heart attack live longer?

Researchers in Sweden chose $1169$persons who had heart attacks at random and asked them about their chocolate consumption in the previous year. The researchers then followed up with these folks to see if they died within the next eight years.

First, we must determine which test should be used in a certain case. There are three tests to complete:

Chi-square goodness-of-fit test, chi-square homogeneity test, and chi-square independence test All of these tests will be detailed for us. A chi-square goodness-of-fit test is used when we are interested in the distribution of a single variable. In this circumstance, we must employ a chi-square test for homogeneity when we are interested in the distribution of two variables with numerous independent samples. We would like to do a chi-square test for independence when we are interested in the distribution of two variables and there is only one sample. We are provided two variables in the present setting: chocolate consumption and death after $8$years.

One random sample of $1169$patients who experienced heart attacks was taken.

As a result, we should perform the Chi-square test to determine independence.

Part (b) Step 1 : Given information

We have to determine which chi-square test is appropriate for given setting.

Part (b) Step 2 : Simplification

Cell phone numbers were previously excluded from random-digit-dialing telephone polls. The poll findings may not represent the full adult population if the opinions of persons who only have cell phones differ from those of people who have landline service. The Pew Research Center questioned separate random samples of cell-only and landline phone users under the age of $30$to ask them about their political party allegiance.

First, we must determine which test should be used in a certain case. There are three tests to complete:

Chi-square goodness-of-fit test, chi-square homogeneity test, and chi-square independence test

All of these tests will be detailed for us. A chi-square goodness-of-fit test is used when we are interested in the distribution of a single variable. In this circumstance, we must employ a chi-square test for homogeneity when we are interested in the distribution of two variables with numerous independent samples. We would like to do a chi-square test for independence when we are interested in the distribution of two variables and there is only one sample. There are two variables in this case. Telephone model and political party There are two separate random samples of cell phone and landline users.

Asaresult,weshouldperformtheChi-squaretesttodeterminehomogeneity.